A Note on The Five-Year Yuga of the Vedāṅga Jyotis.a

B. N. Narahari Achar

1 Introduction

Vedāṅga Jyotis.a (VJ) is the general name by which one refers to the earliest codified texts of astronomy of ancient India, known as the R̊gjyotis.a (R̊J), the Yājus.ajyotis.a (YJ), and the Atharvajyotis.a (AJ). The authorship of the first two is ascribed to Lagadha, whose disciple Śuci composed and preserved the knowledge codified by his celebrated teacher, while the author of the third is unknown. The R̊J consists of 36 verses, the YJ of 44 verses and the AJ of 162 verses divided in to 14 chapters. The R̊J and the YJ recensions are both well known with some variations in readings and have about 30 verses in common. Several scholarly studies of the two recensions have been published^{1}, as also detailed comparative tables of the corresponding verses of both the recensions^{2}. In this note we will concentrate only on the R̊J, using the general term VJ also to mean only R̊J, because, it is the oldest and is of immediate relevance to our purpose. The R̊J preserves the Hindu traditional knowledge of astronomy essential for Vedic sacrifices in a codified form akin to the style of the sūtras, easy for memorization but sometimes difficult for understanding. It packs a wide range of astronomical topics in its 36 verses, some of which are quite obscure. It is more like a pocket reference and gives, among other things, the rules for the determination of proper times for the performance of Vedic rituals. In fact, Śuci declares in R̊J (verse 2), that he is expounding on the science of time, involving the concept and measurement of time at different levels.

One of the distinguishing features of VJ is the use of a period of five years called yuga, which is different from the much larger period also called yuga^{3}, but which came into vogue much later in Indian astronomy in the Siddhānta period. The five-year yuga of VJ consists of 62 candramāsas (synodic months), 1830 days and 1860 tithis (1/30th part of a synodic month) and was taken to commence at the winter solstice. At the time of VJ, winter solstice occurred at the beginning of the first tithi of the śukla paks.a of the month of Māgha. There are two adhimāsas (intercalary months) in a yuga. The sun and the moon are supposed to occupy the same position at the beginning of each subsequent yuga and all the happenings would be repeated in the subsequent yugas in the same way. The astronomical system of VJ was still being followed in India long after the time of Lagadha, although the winter solstice was placed in Śravan.a at the time of Jain astronomy.

Electronic Journal of Vedic Studies (EJVS) 3-4 (1997) pp.21–28

1Weber, A., Über den Veda-kalendar namens Jyotisam, Abhandlungen d. Akad. d. Wiss. (Berlin, 1862); Thibaut, G., “Contributions to the explanation of the jyotis.a-vedāṅga”, Journal of the Asiatic Society of Bengal, xlvi, pp.411–437, 1877; Dvivedin, S., (ed.) Vedāṅga-Jyotis., with Somākara’s commentary (Benares, 1908); Shamasastry, R., Vedāṅga-Jyotis.a with commentary and translation, (Mysore, 1936); Sastry, T. S. K., Vedāṅga-Jyotis.a of Lagadha, (New Delhi, 1985); Yajnik, H. M., Vedāṅga-Jyotis.a, Ahmedabad, 1985; Sen, S. N., in: A concise history of science in India, Bose, D. M., Sen, S. N., and Subbarayappa, B. V.,(ed.), New Delhi, 1971.

2Dixit, S. B., Bhāratīya Jyotis.śāstra, (Prayag, 1957); Yajnik, H. M., Vedāṅga-Jyotis.a, (Ahmedabad, 1985). The list of topics is condensed from Yajnik, H. M., “Vedāṅga-Jyotis.a”, in: Issues in Vedic Astronomy and Astrology, Pandya, H., Dixit, S., and Kansara, N. M., (ed.) (Delhi, 1992), p.52.

3In current parlance, one mahāyuga consisting of kr_{}˚ ta, tretā, dvāpara, and kali yugas lasts for 4,320,000 years.

VJ has often been criticized^{4} for using this yuga period of five years as being “....extremely crude.” The accuracy of VJ is a much discussed affair and it has been argued^{5} that VJ suffered from two main defects. There are actually 1826.2819 days in a yuga of five solar (sidereal) years, and not 1830, as stated in VJ. Therefore, the winter solstice would start four days earlier after each yuga. Furthermore, there are 1830.8961 days in a period of 62 lunar months and not 1830. Hence, there would be a deficit of about one tithi in a yuga of five years. It appears as a mystery why the Indian astronomers continued to use such an absurd system for thousands of years. Is it possible that the ancient Indian astronomers were not aware of these “defects”? Some scholars have indeed assumed just this possibility and have leveled their criticism of VJ, and of Indian astronomy as a whole, on this basis. An extreme example of this type of criticism is found^{6} in the following: “... the acceptance of this cycle by Indians for a period of six or seven centuries or even more demonstrates among other things that they were not interested in performing the simplest acts of observational astronomy.”

This harsh criticism of ancient Indian astronomy in general, and VJ in particular, seems to be a case of uncritical application of current scientific ideas to a work so ancient that some parts of it are still obscure. One may also recall the statement of Whitney regarding VJ: “... and when we come to add that Jyotis.a (i.e.,VJ) has no definable place in Sanskrit literature or relation to the Vedic ceremonial ... we shall see that this famous datum, which has seemed to promise so much, has caused so much labor and discussion, ... is nothing but a delusive phantom.” This is in spite of the fact that VJ it self declares that it is for the purposes of determining the proper times for the Vedic ritual yajña! One should try to understand VJ in its own contemporary context, i.e., in the context of the actions of the Vedic people, their motivation, and the conceptual background of their work.

The purpose of this note is to point out that the concept of the five-year yuga period is much older than VJ itself and was not chosen by Lagadha^{7}. It is intimately connected with the Vedic ritual, yajña, and is but a reflection of a special significance associated with the number five in the Vedic ritual. There is evidence to suggest that the Indian astronomers were in fact aware of the so called “defects,” and took measures to “correct” them. Astronomical observations were routinely made and there existed a group of professional astronomers. Only the fact that VJ is deep rooted in the Vedic ritual of yajña and is an integral part of the same Vedic lore of five-fold manifestations can account for the continued use of VJ over thousands of years, its popularity declining only after the importance of the Vedic ritual yajña itself had declined.

4Pingree, D., “Astronomy and Astrology in India and Iran”, Isis, liv pp.229–246, (1963).

5Sastry, T. S. K., Vedāṅga-Jyotis.a of Lagadha, (New Delhi, 1985); Shukla, K. S., “Main characteristics and achievements of ancient Indian astronomy in historical perspective” in: History of Oriental Astronomy, (ed.)

Swarup, G., Bag, A. K., and Shukla, K. S., Cambridge University Press (Cambridge, 1987).

6Pingree, D., “The Mesopotamian Origin of Early Indian Mathematical Astronomy”, Journal of History of Astronomy, iv, pp.1–12, (1973).

7Pingree in note 6 seems to think there was an Iranian influence on Lagadha.

2 The Yuga Concept:

The yuga period of five years, whose constituent years are called sam .vatsara, parivatsara, idāvatsara, anuvatsara, and idvatsara, has been in use since Vedic times. For example, in R̊gveda (R̊V 7.103.7–8) sam .vatsara and parivatsara are mentioned. The Taittirīya-Sam .hitā (TS 5.5.7.1–3), the Vājasaneyi-Sam .hitā (VS 27.45 and VS 30.16) and the Taittirīya-Brāhman.a (TB 3.4.11 and TB 3.10.4 ) give the names of all the five years, although, there is some variation in the names. The TS calls them sam .vatsara, parivatsara, idāvatsara, iduvatsara, and vatsara, while the VS and the TB call them sam .vatsara, parivatsara, idāvatsara, idvatsara, and vatsara respectively.

The length of the solar year was known to be a little more than 365 days, although the year was roughly taken to consist of 12 months of 30 days each (360 days = sāvana year). Taittirīya-Sam .hitā (TS 7.1.10) says that 5 days more are required over the sāvana year to complete the seasons and that 4 days are too short and 6 days are too long. The scheme of adding intercalary months is also of Vedic origin as is evident from R̊gveda (R̊V 1.25.8). The two intercalary months in a yuga are called am .haspati and sam .sarpa (TS 1.4.14). It is clear, therefore, that the five-year yuga system and the scheme of two intercalary months are much older than R̊J and must have been in practice for a long time before they were codified by Lagadha.

It is also evident that the five-year yuga system with the associated scheme of two adhimāsas continued to be in use in India for a very long time. It also occurs in later texts such as Mahābhārata (pañcame-pañcame vars.e dvau māsāv upajāyate; MBh 4-47), and Kaut.ilya’s Arthaśāstra (pañca sam .vatsaram yugam iti; AŚ 2.20.69.71). Garga-Sam .hitā, and Paitāmaha-Siddhānta all refer to the five-year yuga period of VJ. It has already been noted that the Jain astronomical text, Sūryaprajñapti, mentions it (tā pañca samvaccharā; sūtra 54). The Buddhist text Śārdūlakarn.āvadāna also reflects the use of the five-year yuga of VJ.

3 The Five-year Yuga: Why?

The answer to this question can be found in VJ, its Vedic sources, and in the close connection between jyotis.a and yajña. The purpose of VJ is described in the verses:

kālajñānam . pravaks.yāmi ... yajñārthakālasiddhaye (R̊J 2–3)

“I shall describe [systematically] the science of time for the purpose of determining the appropriate time for [different] yajña.”

VJ is not a mere civil calendar, but one whose purpose is a highly religious one, that of determining the proper times for Vedic rituals. The importance of the Vedic ritual itself is described in the following verse:

vedā hi yajñārtham abhipravr̊ttāh. ... yo jyotis.am . veda sa veda yajñān (R̊J 36)

“The Vedas have indeed been revealed for the purpose of the performance of yajñas. [But the yajñas are to be performed in different segments of time as appropriate.] Therefore, only he who knows [the science of time, namely] jyotis.a, understands fully the [performance of] yajñas.”

Thus VJ not only specifies the role of jyotis.a in the ritual yajña, but describes the interdependence of jyotis.a and yajña also. It also points to a strong connection between the five-year yuga concept and the ritual yajña.

4 Every Thing is Five-fold

The ritual of yajña is central to the Vedas. The basic premise of yajña is to establish explicit equivalence between two different objects by means of ritual action. For example, in Agnicayana, a huge altar consisting of five layers is constructed in the general shape of a falcon, for, “he who is desirous of heaven may construct a falcon-shaped altar.” By ritual action, the equivalence of the following are established: falcon = altar, sacrifice = altar, and finally, sacrificer = altar. Therefore, sacrificer = falcon and hence the sacrificer can fly to heaven. However, if the falcon is not well made the bird will not fly. Altars are constructed according to strict geometrical principles as explained in śulbasūtras. There exists another set of equivalence principles related to astronomical concepts. For example, in Agnicayana, Prajāpati, the Lord of Creation, is identified with time, in fact, the year (prajāpatir eva sam .vatsarah. ..., JB II.393; and: sa es.a prajāpatir eva sam .vatsarah., KB VI.15). Hence, it takes a year from the moment the yajamāna has generated agni in a special pot called ukhā (which he carries around with him), to the culmination in a twelve-day ritual at the end. The altar as well as the yajña is identified with Prajāpati. It is this identification of Prajāpati with time on the one hand and the ritual yajña on the other that holds the secret of the five-year yuga period. The very first verse of R̊J invokes Prajāpati in the following terms:

pañcasam .vatsaramayam . yugādhyaks.am . prajāpatim . dinartvayanamāsāṅgam . pran.amya śirasā śucih. ... (R̊J 1) “(I, ) Śuci, salute with a bowed head, Prajāpati, who is the embodiment of the fiveyear period and who presides over the yuga, and who has for his limbs, time segments like the day, the seasons, the [northerly and the southerly] courses of the Sun, and the month...”

This characterization of Prajāpati by a five-fold embodiment in time, is also reflected in the fivelayer structure of the altar which is also identified with him. In fact, the five brick layers of the altar in Agnicayana have the same names as the years in a five-year yuga period. A fivefold characterization is a preferred way of discussing items with reference to the ritual yajña (i.e., adhiyajña). There are five yajñas: bhūtayajña, manus.yayajña, pitr̊yajña, devayajña, and brahmayajña. The altars can also be five in number: gārhapatya, āhavanīya, daks.in.āgni, sabhya, and āvasathya. There are five requisite materials for the yajña, which are described in ŚB (ŚB 1.1.1–8), and it is said there that the sacrificer gathers these five materials (“pañcasam .bhārān sam .bharati”).

The five-fold nature goes beyond the ritual (referred to by adhiyajña) to the material world (referred to by adhibhūta) and also to the Self (referred to by adhyātma). This is all described in TU beginning with the following declaration:

athātah. sam .hitāyā upanis.adam . vyākhyāsyāmah. pañcasv adhikaran.es.u (TU 1.3.1)

“Now we shall explain the upanis.ad of the smāhitā under five headings”

It is said in (TU 1.7.1):

pr̊thivy antariks.am . dyaur diśo ’vāntaradiśah. agnir vāyur ādityaś candramā naks.atrān.i āpa os.adhayo vanaspataya ākāśa ātmā ity adhibhūtam . “The earth, the sky (antariks.a), the heaven, the main quarters and the intermediate quarters (which constitute the set of five worlds); fire, air, sun, moon and the stars (the set of five-devatās); water, plants, trees, ether and the ātman (the set of five living beings); thus with regard to the material existence.”

Described above are three sets of five members each as external and gross embodiment of the Supreme. This is followed in (TU 1.7.2) by:

athādyātmam prān.o vyāno ’pāna udānas samānaś caks.us śrotram . mano vāk tvak carma mām .sam . snāvāsthi majjā “Now, to the self; prān.a, vyāna, apāna, udāna, and samāna (the set of five vital airs), eyes, ears, mind, speech, and touch (the set of five senses), skin, flesh, muscle, bone, and marrow (the set of five constituent elements of the body).”

This enumerates the three sets of five objects each, which are internal and subtle embodiment of the Supreme. Again, in (TU 1.7.3):

etad adhividhāya r̊śir avocat pāṅktam . vā idam . sarvam . pāṅktenaiva pāṅktam . spr̊n.oti “After having analyzed all this the sage declared: all this is verily pāṅkta (five-fold); by the pāṅkta, indeed, does one secure the pāṅkta”

Thus the TU declares every thing as having a five-fold nature and later, goes on to describe the five kośas (sheaths) that cover the Self as the annamaya, prān.amaya, manomaya, vijñānamaya, and ānandamaya kośās. This is also echoed in BU (BU 1.4.17):

sa es.a pāṅkto yajñah. pāṅktah. paśavah. pāṅktah. purus.ah. pāṅktam idam . sarvam . yad idam . kiñca “so this yajña is five-fold, five-fold are the animals, five-fold is the person, five-fold is all this world, whatever there is.”

Thus śruti declares that there is a five-fold principle that pervades the entire universe and that the principle is manifest in the external and gross aspects as well as in the internal and subtle aspects.

5 Time Units in VJ

While the main attention so far has been focused on the five-year yuga period, there are other intervals of time, such as cāndramāsa, tithi, kalā, muhūrta, and kās.t.hā that are referred to in R̊J. The relationships among these time units can also be found in R̊J.

124 kās.t.hās  = 1 kalā
20 and 1/10 kalās  = 1 muhūrta
30 muhūrtas = 1 ahorātra (day and night)
2 parvans = 1 cāndramāsa
2 months  = 1 r̊tu
2 ayanas  = 1 year.

It is interesting to note that the smallest unit of time, kās.t.hā, is given in terms of the duration of five aks.aras:

kās.t.hāh. pañcāks.arah. smr̊tā\begin{matrix}h \\ . \end{matrix} (R̊J 18)

The same five-fold principle is operating both at the subtle (kās.t.hā) and at the gross (yuga) level of measurement of time and time itself may be regarded as “pāṅkta”. This idea is strengthened in view of the paṅkti-meter consisting of five pādas of eight syllables each. The śruti declares, “fivefooted is the paṅkti-meter and yajña is a ‘pāṅkta.’ ” It may be noted in passing that according to Śatapatha-Brāhman.a (ŚB 10.4.2.23), the number of paṅktis in R̊gveda^{8} is equal to 10800; this is equal to the number of muhūrtas in a year and also to the number of bricks in the altar. The five-year yuga is simply another manifestation of “pāṅktam idam . sarvam .” and it is this strong dictum of the śruti that perpetuated the use of the five-year yuga period for such a long time.

6 “Accuracy” of VJ

It must have been known even in those early days that 62 synodic months take almost a day more than the 1830 days given in VJ, because at the end of one yuga, must have been observed to occur on the day next to the 1830th. Observation at the end of the next yuga would have clearly shown this (because of the cumulative error), the moon would have been well up in the sky at sunrise showing the day to be caturdaśī or even trayodaśī, so that amāvāsya would occur one or two days later. The priests would never have failed to notice this, because, it was their duty to observe the last disappearance of the old moon and the first appearance of the new moon. This is connected with the “upavasatha” and referred to in the following verse:

caturdaśīm upavasathas tathābhavet yathodito dinam upaiti candramāh.

māghaśuklāhniko yuṅkte śravis.t.hāyām . ca vārs.ikī\begin{matrix}m \\ . \end{matrix} (R̊J 34)

“That caturdaśī tithi on which the moon rises [almost] as the sun rises is the upavasatha. [Any characteristic of] the first day of the bright fortnight of the month of Māgha links [the naks.atra of] the last day of the previous year [Śravan.a] with śravis.t.ha [i.e., it is common to both].”

The upavasatha day is the day of pin.d.apitr̊yajña, and the day previous to that is ādhāna or dīks.ā day and the next day is the is.t.i day. Moon rising almost at sunrise indicates that the time is near new moon. By contrast, if the moon rises well before the sun rises, it is technically called uddr̊s.t.a, and all excepting Vājasaneyīs and Baudhāyanas have to perform an expiatory rite, or prāyaścitta, to nullify the evil that will accrue and perform punarādhāna, if the ādhāna had already been done the previous day. This shows that the priests had to be very careful to avoid such a thing happening and they must have had rules formed from observations over a long time to fix the calendar. The fact that the Vedic priests did indeed make observations is evident from the statement in the verse R̊J 24 regarding ascertaining calculations by observations (ity upāya samuddeśah. ...). The fact that there were astronomers who made observations is attested to by the reference to naks.atradarśa, an observer of stars, in VS (VS 30.10) and to naks.atravidyā, the discipline of astronomy, in Chāndogya-Upanis.ad (CU 7.1.2; CU 7.7.1).

8This is based on the syllable count of 432000, given in the ŚB; but, the actual number of syllables in the canonical text is far less. A full discussion of this point, however, is beyond the scope of the present paper.

It has been suggested that a day could have been tacitly added to the yuga after its end (just as we add a day in the leap year) and not counted in the calculation. This would certainly avoid the most patent discrepancy. However, as 62 synodic months = 1830.8965 days, another type of error will accumulate and an intercalary month would have to be dropped after 6 yugas and another intercalary month after 7 yugas, and this has to be repeated. It may be noted that it is not necessary to know this rule to drop the intercalation. Mere observation of the moon in the śravis.t.ha region of the sky would have shown the need for an intercalation^{9}.

7 Conclusions

We have clearly demonstrated that the five-year yuga cycle of VJ is much older than VJ and was not selected by Lagadha. It continued to be in use for a very long time after VJ, its popularity is due to the Vedic dictum of being pāṅkta. Vedic priests did make observations and must have formulated rules for overcoming, as far as possible, whatever calendrical shortcomings a five-year cycle might imply. This would have been necessary to avoid penalties in obeying the requirements of upavasatha. The Vedic dictum of pāṅkta would thus explain the enigma of the five-year yuga which has puzzled the scholars of VJ for over a century. When viewed in the light of “pāṅkta” dictum, the criticism of Pingree would not appear to be valid.

List of Abbreviations

AJ Atharva-Jyotis.a

AS Arthaśāstra of Kaut.ilya

BU Br̊hadāran.yaka-Upanis.ad

JB Jaiminīya-Brāhman.a

KB Kaus.ītaki-Brāhman.a

MB Mahābhārata R̊J R̊gjyotis.a R̊V R̊gveda TB Taittirīya-Brāhman.a TS Taittirīya-Sam .hitā TU Taittirīya-Upanis.ad VJ Vedāṅga-Jyotis.a, here also used for R̊J VS Vājasaneyi-Sam .hitā YJ Yājus.ajyotis.a ŚB Śatapatha-Brāhman.a

9Sastry, T. S. K. 1985; in fact, Muslims do so even today by observing the crescent moon.